Yes, you do have lounge access. You can ask UA, when you check in, if they will link the tickets and check you all the way through to Scotland. I've been able to do this in years past, but don't have any recent experiences.

If UA will not check you in all the way through, and you have luggage, you'll need to claim the bags, clear customs, change terminals, and check back in. I'd probably allow at least 4 hours if you need to do that. Depending when you arrive the lines can be long.

You do have some risk that if you misconnect due to a UA delay, that BMI does not need to reaccomodate you, and you will be at their mercy to get you on the next available flight out, assuming seats are available. I don't do these any longer (separate tickets) preferring to overnight in London and then fly out the following day, to take some of the risk away.

If, for some reason, BMI cannot get you to Scotland due to a late arrival, you do have bus and train options if last minutes tickets are outside your budget. Check the National Express web site for the bus options.